a bibliography of publications about the computation of ... · a bibliography of publications about...

A Bibliography of Publications about the Computation of

Elementary Functions in Computer Programming

Languages

Nelson H. F. BeebeUniversity of Utah

Department of Mathematics, 110 LCB155 S 1400 E RM 233

Salt Lake City, UT 84112-0090USA

Tel: +1 801 581 5254FAX: +1 801 581 4148

E-mail: [email protected], [email protected],[email protected] (Internet)

WWW URL: http://www.math.utah.edu/~beebe/

12 June 2009Version 3.24

Title word cross-reference

(0, 2) [GRS87]. (n, 1) [Kra85b].(n, 2) [Kra85a].−∞ < N < +∞ [Kog57, Kog58b].0 < N < 1 [Kog58a]. 1/9 [Mag94]. 2 [Bak73].2p [Mer94]. 4 [NL99]. 8 [HF95].[−1, 1] [HR88]. arc tan Z [Luk57]. B [Wen09].χ2 [Fet79]. cos [Tur69]. cosh z = az [Fet76].cos N [Kog59]. cosx [Bar72, Bar72].e−x [Bar72]. e−z [Sie76]. eN [Kog57].ex [Bar72]. exp(Bt) [PN85]. Γ [BB82, BF92].I0(x) [Bla74]. I0(ξ) [Las82]. I1(x) [Bla74].In(b) = 2π−1

∫ ∞0

(sinx

x

)n cos(bx)dx [Tho66].In(b) = 2

π

∫ ∞0

(sin x

x

)n cos bxdx [Fet67].

In(b) = 2π

∫ ∞0

(sin x

x

)n

cos(bx)dx [MR65].

In(X) [D. 44].∫ ∞0

t2α−1Jν(x√

1+t2)(1+t2)α+β−1 dt [Sch78a].∫ ∞

0t2α−1(1+t2)1−α−βJν(x

√1 + t2)dt [Gla79].∫ ∞

xe−t2/2tpdt, x > 0, p [DiD78].∫ π/2

0J2

0 (γ sin x)dx [SF87].∫ π/2

0J2

ν (λ cos θ)dθ [Won88]. J−ν(x) [CK79].J0(x) [WBR82]. J1(x) [WBR82].Jn(z) [CM83]. k [Bas01].Kn(Z) [Par72, LG79]. Kν(t)/Iν(t) [LL72].Kin(x) [BEJ78]. L [ZSA86]. Lp [Hei88].log Z [Luk57]. M [Kog59]. n [CL00, Kog59].ν [CK79]. O(N2/ log3/2 N) [SR81].O(n3L) [Gon89]. φ [Pro88]. π [BBB89].ψ [Gla66]. ψ(x) [DR98].

1

2

ψ(x) − θ(x) [Per85, Per87].ψ(x; 3, l) [McC84]. ψ(z) [McC81]. q [Bor88].R2 [Bos89]. sin [Tur69]. sinN [Kog59].sinx [Bar72, Bar72].sin z = az, cos z = az [Fet76].∑∞

n=1 np−1E∗n(f) < ∞ [HS83]. θ [Phi60].

θ(x; 3, l) [McC84]. U(a, x) [GST06a].V (a, x) [GST06a]. xn [McC77].Y0(x) [WBR82]. Y1(x) [WBR82]. Z [Som82].Z2 [Lef05].

-discrepancy [Pro88].-distribution [Fet79]. -elementary [Bor88].-Function [Gla66]. -functions [BB82].-interpolation [GRS87].-saturation [Hei88]. -select [CL00].-spaces [Som82]. -zeros [CK79].

/ [Tur69].

1 [Fro63]. 10th [KM91]. 11th [SIJ93].121 [Laz85]. 121-122 [Laz85]. 122 [Laz85].12th [KM95]. 13th [LMT97].144 [ACG+87]. 14th [KK99]. 15th [BC01].1604 [Mae60]. 167 [PZ95]. 17th [IEE05].18-19 [IEE81]. 1975 [Tra76].1983/84 [Laz85]. 1996 [Boi97].1999 [DIW00]. 19th [BCDH09].

2001 [BC01]. 2006 [Ano06].

30 [ACG+87]. 30-ns [MIT+95]. 32 [ASA06].33rd [Spr00]. 34 [Fra81]. 3800 [WOG95].

44 [Per87]. 4th [IEE78].

55-b [MIT+95]. 5th [IEE81].

64 [HKST99].

723 [And00]. 754 [Hou81]. 757 [Mac96].77 [WNO94]. 794 [Wie99]. 7th [Ano06].

804 [Alh00a]. 814 [Smi01]. 819 [GST02].

81f [Fra81]. 831 [GST04a]. 838 [Fab04].850 [GST06a]. 86k [Per87]. 877 [Kod08].’89 [ACM89].

90 [Tho97a]. ’91 [IEE91]. 9th [ES89].

A-Priori [Kra87]. A.F. [Leh83b].Abramowitz [Dav59]. abstracts [Spr00].Academy [Mil75]. Accelerating [BMR04].Acceleration [IBM05].Accuracy [Sal51b, Rot71].Accurate [MNP83]. Achieving [Gal85].ACM [Mor64]. ACM-SIGSAM [ACM89].Ada [Mat87]. adaptive [Was89].Addendum [Fra81]. adders [CP99].Addition [SS97b]. Adelaide [KK99].Ado [Kah87]. advance [BMR04].Advanced [Luk99]. ahnliche [Vol83].Airy [HB75]. AIZ [GST02].Albuquerque [IEE91]. algebra [Tre80].Algebraic [Ris79]. algebras [Hai60].Algorithm [Mor64, Fil66].Algorithmen [Vol83]. algorithmic [Che81].Algorithms [DeL70]. Algorithmus [Fil66].allgemeiner [von80]. AMD [Obe99].AMD-K7TM [Obe99]. Among [JMMW79].analog [HFS99]. Analogue [SR53].analysis [LCJ63]. analytic [BL71, Tra76].Analytical [Sho60]. ANL [Kuk66].Annual [Spr00]. Anomalous [Gau77].APMathLib [ZOHR01].application [EC79].Application-Specific [T+97].Approach [Gal85]. approximants [DF78].Approximate [Mar72].approximating [Epp89].approximation [Peı63].approximation-theoretic [VB81].approximations [Cle54].approximators [HSW89]. April [Tra76].Aptitude [Vol83]. Arbitrary [Rot71].architecture [MS82].architectures [MMH93]. Arcsin [Kog58a].Arctan [Kog58b]. arctangent [JL94].

3

arctangents [Car72]. area [SR81].Area-efficient [Tom00].Argument [Bar61]. Arguments [R. 43].ARITH [BC01]. ARITH-15 [BC01].ARITH-17 [IEE05].arithmetic [MT72, Atk79].Arithmetic-Geometric [BB84].Arithmetique [Ber84]. Array [Dav81].arrays [EM86]. Art [IP87].ASIC [WMDM92]. Asilomar [Sin95].Assessment [Boi97]. associated [Sai89].asymptotic [Mac72].Asymptotically [Wan82].asymptotics [Tem86]. Atlantic [AFI71].Atlas [SO87]. attempt [Che81].August [Mar85]. Australia [Lav80].autocorrection [Lit93]. automatic [Lin57].

b [MIT+95]. background [Kog89].Backward [OS72]. Bad [MT85].Baltimore [IEE99]. Bandwidth [Far81].Based [KZ90]. Basic [Kuk71].basis [Mul85a]. Bath [KM95].BCY [Che81]. Be [PW76]. beach [Ehr89].behaved [Vai89]. beliebige [Kra87].beliebigen [Bra87]. beliebiger [Rot71].Benchmarks [WOG95].Berechnung [Fil66, von84].Berkeley [Liu87]. Bernstein [Bor82].besonderer [Vol83]. Bessel [BA44].Best [Nin70]. beta [Tem75].Betriebssystems [Rot70]. better [LM00].between [Car69]. Bibliography [Ful80].Bickley [BEJ78]. bicomplex [Tre80].biharmonic [Mon83]. billion [BBB89].Binary [DeL70]. Bipartite [SS97a].Birmingham [IP87]. BIT [Fro63].bivariate [LW89]. BIZ [GST02].BKM [BKM94]. BLAST [Has00a].Block [Cas83]. Boolean [Bel89].Boost [BD99]. bootstrap [LW89].Boston [ACM87]. Boulder [Mul82].bound [Cha82]. boundary [JS89].boundary-value [JS89]. bounded [HR88].

Bounding [HKA93]. Bounds [Olv88].Bourbaki [Laz85]. box [DR89].Branch [Kah82]. Build [Sal92].bulk [AM89]. Bureau [Mul82].

C [Sch88]. C9X [McC02]. CA [IEE78].Cairo [Wah04]. cake [Bel89].calcul [Mul85b]. calculateurs [Ber84].Calculating [Sal51a]. Calculation [SR53].calculations [Sal76]. calculus [SO89].Cape [IEE05]. Caratheodory [Mag94].cardinality [Was89]. carefully [Wil96].Carnegie [Tra76]. Cascaded [KNS95].Case [Cas83]. Cases [LM03]. CD [Spr00].CD-ROM [Spr00]. CELEFUNT [Cod91].cell [JL94]. cellular [CL95].censoring [Ruy89]. centennial [AGA+80].center-unstable [AGH89].century [Gau94]. certain [Abr45].Certified [CJL09]. Cesaro [MS87].chain [Wil96]. chaos [PH90].characteristic [McN73].Characterizing [Kee82].Chebyshev [Fro63, Bar61].chemists [Wen09]. Chinese [Liu93, Che81].choice [Ge89]. circuit [Bel89].Circuits [DM88a]. City [AFI71].Clarification [ACG+87]. Class [DeL70].classes [Kaz65]. classical [Tem96].Clever [Kah04]. closed [Dav88].CMOS [TRHH94]. co [DMS95, USE88].co-processor [DMS95]. Cod [IEE05].Codes [FLR03]. coefficients [FW80].Collection [WNO94]. Collective [Sti88].Colorado [Mul82, Luk99].combination [Lit83]. Combined [LM95].combining [MI97]. Comments [Tra60].Common [BK78]. Comp [Fra81].compact [Whi82]. comparison [LMS73].Comparisons [FLR03]. Compilers [BD99].complement [CL94a].complementary [Zak69]. complete [RT89].Complex [Sal51a].Complex-Valued [Mat04].

4

Complexities [NS09]. complexity [Bre75].complying [AHM+98].Component [vRdL88].Computation [SR53].computations [Dan77]. compute [BBB89].Computer [Kog57].computer-oriented [AGA+80].computers [Has55]. Computing [Vol59].concept [Gon52b]. Concerning [Wre68].condition [HS83]. Congress [Lav80].conjugate [MS87]. connect [CK88].connection [Car69]. constant [Blo88].constants [CB87]. Constrained [MT72].Constraints [Kuk71].constructing [Kai89].construction [Dan77]. contained [CC69].containing [Mak65]. Contents [Ful81b].continued [Sar60].Continued-Fraction [Smi95].continuous [PS78]. Contour [ST07].contoured [Was89]. Contributions [Ng84].control [Roc82, Mae60].convergence [PKP74].convergent [McC81]. Converging [ITY95].convex [Fuk83]. conveyors [Liu95].Coprocessor [KZ90].CORDIC [Vol59, Vol83].CORDIC-Algorithmen [Mul90].Correct [LM03]. Correctly [Ziv91].Correctness [CHGM99].correspondence [vRdL88].Corrigenda [Ano94]. corrigendum [Fra81].Cosine [Tha61]. Cost [Dan82]. Cost/performance [CL00]. CoStLy [Neh07].Coulomb [Ike75]. course [BW00].Cray [???90, KB90]. crunching [Atk79].current [Liu95]. curves [Nis94].Cuts [Kah82]. cylinder [Kre89].Cylindrical [Kod08]. [LCJ63].

d’apres [Laz85]. Data [Mae60].datapath [CCCP99].Datenformate [Kra87].Davenport [Laz85]. December [ACM87].

Decimal [Har09a].Defektberechnung [Mul90].defined [Tre80]. definite [Gla74].definition [BL71]. Degenerate [PS79].degree [Tes69]. demonstration [CCC96].Denominator [BM04]. density [McN73].Denver [USE88]. dependent [Kre89].Depth [OTY91]. derivative [Wen64].derivatives [Bus74]. Design [SS94].designing [WN03]. designs [Sg92].Desirable [Hul78]. Determinant [CT88].Determination [Liu93].Deuxiemes [AEF92]. Develop [ACG+87].diagonal [Kra89]. difference [CH78].differences [MNP83]. different [Her71].differentiable [Pro87].differential [Arm82]. differently [DM91].Differentsiruemye [PS93].differintegrations [Nis84].Difficulty [Tur69]. Digamma [Moo67].digit [PKP74]. digit-by-digit [LP83].digit-recurrence [LE93]. digital [Has55].digits [BBB89]. dimension [vRdL88].dimensional [VB81]. Dirac [Fer86].direction [DR89]. discrepancy [Pro88].discrete [Tur72]. dispersion [CH78].displacement [YH89]. Distance [Lef05].distributed-memory [Tak00].distributions [Wan82]. divide [MM92].divided [MNP83]. Division [Sar59].division/square [LM99].Divisionless [Sar60]. divisor [BMR04].DLMF [Loz00]. do [Wen09].Documentation [Rot70].Dokumentation [Rot70]. domains [Shi93].Double [Spe72]. double-length [HHv+73].Driven [Tan89a]. drobno [Saa91].drobno-ratsional’nykh [Saa91].DSP [MKY92]. DSP-Oriented [MKY92].dual [KMY89]. dual-rail [MI97].dynamic [Kra88]. dynamics [AGH89].dynamischer [Mul90]. Dzjadik [Kon76].

edge [Mit92]. effect [Lit93].

5

Effective [Kra85b].effektivnom [DZKK77]. Efficient [Spi61].efficiently [NL94]. Egypt [Wah04].Eignung [Vol83]. Einbettung [von80].einfacher [von84]. einiger [Fil66].Electronic [Kog57]. element [LG79].Elementaarsed [Jur66].elementaires [Ber84].elementaren [Rot71].Elementarer [Emd45].elementarnykh [LCJ63].Elementary [Rit25].Elementary-Function [BBM84].elements [Mus87]. elliptic [Nis94].elliptically [Was89]. Embedding [von80].empirical [Ruy89]. encoding [ZXBZH01].end [Fet74]. energy [Sti88].engineers [Lau95]. England [KM95].English [AEF92]. Enhancement [Boi97].ensembles [AEF92]. entire [Zal89].equation [Mon83]. Equations [Lir71].equivalence [Her71]. ergodic [Kra89].ERL [GEK04]. Erlang [Whi63].Erratum [Fro63]. Error [Sal51a].Errors [CJL09]. Estimates [Fra78].Estimation [CKL89]. estimators [Wan82].Estonian [Jur66]. Euler [Dav59].evaluate [McC77]. Evaluating [Whi63].Evaluation [Bar61]. exact [BWKM91].Exactly [SS94]. examine [Wil96].Excellence [Lid01]. Exception [HFT94].exchange [SR81]. Execution [Bai93].Existence [Wan74]. expansion [Fet79].Expansions [SR53]. Explanatory [Ful81b].explicit [OG82]. Expm1 [Tan92].exponential [Fog51].Exponentials [Che72].exponentiation [CC69].expressions [Sho60]. extended [KA71].extended-precision [KA71].Extended-Range [SOL81].Extension [Rus88]. extensions [Ker83].extraction [GRHL96].

Faber [Ell83]. failure [Wan82].Fall [AFI69]. familiar [BB88].Fast [Bre76a]. Fast-Start [Mar05].faster [DM91]. fatigue [Sob88].Favard [GS82]. feasibility [Via89].feedforward [HSW89].Fehlerabschatzungen [Kra87].Fejer [Mag94]. Fermi [Fer86].Fermi-Dirac [Fer86]. field [Ehr89].Filter [MKY92]. find [LG79].finding [Bre75]. finite [Fog51].first [Cha82]. fitting [Phi79]. fixed [Vav89].floating [MT72]. floating-point [MT72].flous [AEF92]. FNLIB [Ful81b].following [Laz85]. fonctions [Ber84].form [Dav88]. Format [MMNP91].Formats [Kra87]. Formula [Spi71].formulae [Akr85]. Formulas [Sal51a].FORTRAN [Kuk66].Fortran-77 [KDDH94]. Forum [IEE99].four [DMS95]. four-quadrant [HFS99].Fourier [MS87]. Fourth [Atk79].FPGA [TVG00]. FPGA-based [DR04].FPGAs [WN03]. FPU [AHM+98].fractals [PH90]. Fraction [Spi61].fractional [Abr45].Fractions [Mor64, Spe72]. French [Ber84].Fresnel [And00]. FRG [MT85].Fukuoka [Ano91]. full [AHM+98].Function [D. 44]. functional [vRdL88].functionals [Deh89].functions [Rit25, Loz03].Fundamentals [AGA+80].Funktionen [Fil66, Emd45].funktsii [PS93, PS93].funktsioonid [Jur66].funktsioonide [Jur66]. funktsiı [LCJ63].funktsiı. [DZKK77].funktsiımetodom [LP83].funktsiıs [Saa91]. Further [Laf84].fuzzy [DP92].

Gal [SZ05]. gamma [Dav59, Har97].gamma-ray [Phi79]. gate [LE93].

6

Gaussian [Akr85]. Gautschi [Ker83].genauer [von84]. Genauigkeit [Rot71].general [Gon52b]. generalization [Rac82].Generalized [Bur64]. generating [Olv80].Generation [SA57]. generator [War75].generators [AHM+98]. Generic [Tan88].genetic [Tan87]. Geometric [BB84].geometry [Sti88]. German [Emd45].GEV [Gom89]. Gleitpunktrastern [Bra87].Goldschmidt [EIM+00]. Good [Gal85].Gopengauz [CG89].Gopengauz-type [CG89].gradient [Mit92]. Graph [NS09].Graph-Based [NS09]. Graphs [JMMW79].Green [JS89]. Group [???90].groups [CK88]. Grove [Sin95].growth [Bos89]. guaranteed [Loe01].Guide [BA44]. guidebook [Tho97b].Gumbel [Gom89].

Half [Lir71]. half-century [Gau94].Handbook [LCY65]. Handling [HFT94].Hankel [Mac72]. Hankel-norm [Glo89].Hardware [Mar72].Hardware-based [WG91].hardware-oriented [OY91].Hardwired [DM88b]. Hausdorff [Gre82].having [Bos89]. Hawaii [MS94, Spr00].hazard [Ruy89]. held [Tra76].hereditary [Roc82]. hierarchies [Her71].hierarchy [Her69]. High [Sal51b, Bra87].High-Accuracy [Bra87].high-order [Sch93a].high-performance [MM92].High-precision [FW80].High-radix [Sch93a].High-Speed [SW99b]. higher [Car69].Highly [Lut95]. Hilfe [Fil66].historical [Dav59]. history [Wen09].Hitachi [WOG95]. Hochgenaue [Bra87].Hong [DIW00]. honneur [AEF92].honor [AEF92]. Howland [LW82].HP [LMOT01]. HP-UX [LMOT01].hybrid [CP99]. Hydra [Rot70].

Hyperbolic [Tha61]. hypercube [Tan87].Hypergeometric [Bus76].hypersurfaces [Sti88].

IA [HKST99]. IA-32 [ASA06].IA-64 [HKST99]. IBM [ACG+86].ICEEC’04 [Wah04].identification [Roc82]. identity [EC79].IEEE [Hou81]. IEEE-754 [AHM+98].IFIP [Boi97, Lav80]. II [Luk71b].III [Luk72]. illustrated [Tho97b].IMA [IP87]. IMA/SIAM [IP87].image [JL94]. Imaginary [Bar61].immiscible [YH89].Implementation [von80].Implementations [Tan90c].Implementierung [von80].Implementing [Tho87]. Improved [Nin70].Improvement [OGWY94].Improving [EIM+00]. incident [Ehr89].Inclusion [Cri82]. Incomplete [Bar61].Incorporated [PW76]. increasing [Wan82].Indefinite [CK89]. Independent [Fra65].Industry [BBM84]. Inequalities [Nas74].inequality [Rac82]. Infinite [Lir71].Infinitely [IM99]. Initial [Cas83].Initiative [Loz00]. inner [AB88].insertion [OJ04]. institutions [BL71].Instruction [PW76]. Integer [Alh00b].Integrable [PS93]. integral [Dav59].integrals [Mak65]. integrated [DM88a].Integration [Cas83].Integriruemye [PS93]. Integro [Mil85].Integro-Exponential [Mil85].Intel [ASA06]. interact [Wen09].Interactions [BJG+99].interference [Dem89]. interior [KMY89].Interior-Point [Meg89b].interpolation [GRS87].Interpolator [POMB05]. interval [Mar81].Intervallargumente [Kra87].Intervalle [Bra87]. intervals [EMR82b].INTLIB [KDDH92]. intrinsic [Mil89].Introduction [Dri91d]. inverfc [Phi60].

7

Inverse [LaF54, Kra87].Inverse-Square-Root [KNS95].inverses [Rit25]. Inversion [Tem92].Investigation [Mak65]. Involving [Gla66].Irish [Mil75]. isn’t [Wil96].ISSAC [ACM89]. issues [BH01].Itanium [LMOT01]. Iterated [Tha61].Iteration [Nin70]. iterations [HHR00].Iterative [KNS95]. IV [Dun94a].IX [Luk99]. izbytochnykh [LP83].

J [ACG+87]. Jackson [CK88].Jacobi [Spe72]. Jacobi-fractions [Spe72].January [Mul82]. Japanese [OGWY94].Java [Lau04]. Jersey [AFI71].journees [AEF92]. July [Mar85].June [AGA+80].

K5 [LASC95]. K7TM [Obe99].Kaufman [AEF92]. Kaufmann [AEF92].kernels [Mus87]. kind [Gla74].Kingdom [Boi97]. known [BMR04].Komlos [Ein89].Kompleksmuutuja [Jur66].komplexe [Bra87]. Kong [DIW00].Kummer [Gau77]. Kuramoto [AGH89].Kuramoto-Sivashinsky [AGH89].Kutta [Cas83].

Lagrange [Blo88]. Laguerre [GM84].Lanczos [Pug04]. language [Che81].Large [GT58]. Last [Ziv91].Latency [ALMN05]. Lattice [SLZ05].law [Deh89]. layer [Bel89]. layout [SR81].learning [BL71]. least [Rei86].Lebesgue [Blo88]. Legendre [Lew69].length [HHv+73, von84].Leonhard [Dav59]. Lerch [GS88].Less [Bak92a]. libm [LMOT01].Libraries [MMNP91, Kuk71].Library [Kuk66]. Lie [CK88].likelihood [Gom89]. limit [LW89].limited [EM03]. Limits [Gon52b].line [Fro63]. Linear [Jam81].

linear-threshold [Lit89].linearized [Ehr89]. lines [BF92].link [Wil96]. Linux [IBM05].Lipschitz [Som82]. LNS [DMS95].local [Kee82]. locally [Vai89].Log [OTY91, Har97]. Log-Depth [OTY91].log-Gamma [Har97]. Logarithm [CH67].Logarithmic [Fog51]. logarithms [Car72].Lommel [FS92]. Lookahead [KNS95].Lookup [Tan91b]. loop [Mim88].Low [Car75]. Low-Order [Car75].low-power [KP98]. lower [Bel89].lower-bounds-to-circuit-size [Bel89].LSI [Atk79].

Macdonald [FLR03]. machine [Bel89].machines [Lin57]. macrocell [AHM+98].MAD [BBC+91]. Madelung [CB87].Major [Ein89]. Make [Wil96].manifold [AGH89]. Mantissa [von84].Mantissenlange [von84]. Manual [CW80].March [MT85]. Markov [Rac82].Martingale [RT89]. Maryland [IEE99].Massachusetts [ACM87].massively [BBC+91].massively-parallel [BBC+91].Matematicheskiıanaliz [LCJ63].Mathematica [Tho97b].Mathematical [IBM05].mathematicians [Wen09].Mathematics [Gau94]. Mathieu [Alh00b].Matrices [Leh96]. matrix [Ng84].Maui [Spr00]. maximal [von84].Maximally [von84]. Maximum [vR89].maximum-redundancy [HF95].May [AFI71]. Mean [BB84].Means [Fil66]. Measurement [BDL+01].Measurements [Lid01]. measures [Was89].media [YH89]. Melbourne [Lav80].Mellon [Tra76]. Memoriam [Dav59].memory [Kog89]. mesh [DR89].Method [LaF54]. methodologie [Mul86].methodology [Mul86]. Methods [Fra65].metric [Som82]. Mexico [IEE91].

8

MHz [PZ95]. Michigan [IEE81].micro [Ber84]. microcomputer [Mil89].Microcomputers [Vol83].microprocessor [Obe99].microprogramming [Hit75].Mikrorechner [Vol83]. Military [MC87].Milton [Dav59]. mincing [Bel89].mini [Ber84]. mini-micro [Ber84].Miniaturized [Luk71a]. Minimax [Fra65].minimization [Dan77].Minkowski [Kra89]. Mirakyan [Sun88].MISCFUN [Mac96]. Mises [Deh89].Mistake [Lit89]. mittels [von80].mnogochlenami [DZKK77].Mnogoznachnye [Bar72]. Model [Fra78].models [Ric88]. modern [BL71].Modification [WS06].modified [Par72, GST04a].modular [BBB89]. module [MM92].modulo [BH99]. Modulus [CS83].moment [Gre82]. Moments [LL72].Monica [IEE78]. monotone [Dun87a].most [LM07]. MP [KB90]. MR [Fra81].Much [Kah87].Multidimensional [Dem89].Multilayer [HSW89]. Multiplace [Bar72].Multiple [Bre75].Multiple-precision [Bre75].multiplication [McC77].multiplier [WG92]. Multipliers [Ahm89].multiply [MM92]. Multiprecision [Bai93].Multistep [Ske86a]. multivariate [Rac82].Murphy [Mei83]. must [Wil96].

N [Kog58b]. Nancy [Ano06].Narrowing [HJ96]. nationales [AEF92].Natural [CH67]. NBS [Loz97b].Near [Fra65]. near-field [Ehr89].Near-Minimax [Fra65]. Need [BBM84].Needs [Loz94]. Nepreryvnye [PS93].Nested [Dom03]. network [SR81].networks [HSW89]. Neuenahr [MT85].Nevada [AFI69]. Newman [Bor82].Newton [Nin70]. Newton-type [Vai89].

Nimes [AEF92]. Ninth [Sin95].NIST [Loz03]. no [Fra81]. nodes [Ben98].nombres [Mul85b]. Non [R. 43].non-characteristic [AB88].non-restoring [LC96].Non-Sexagesimal [R. 43].nonconvex [Ubh89]. nonlinear [Mus87].Nonnegative [Kod08].Nonstandard [Ric88]. Nonstiff [Cas83].nonuniformly [FK88]. Norfolk [S+93].norm [Akr85]. Normal [Car75].Normalized [SOL81]. normally [Ehr89].norms [Mag94]. Note [D. 44].Notes [SF59]. Nothing [Kah87].Notices [Moo67]. Novel [Bas01].November [AFI69, AEF92].novembre [AEF92]. NP [RT89].NP-complete [RT89]. ns [MIT+95].number [LP83]. numbers [Nag68].Numerics [Nav83].

Ob [DZKK77]. Objectives [Kuk71].occasion [AGA+80]. October [Lav80].ODEs [LO93].Odnomernyımatematicheskiıanaliz [PS93].Off [Kuk71]. on-line [DHM89]. one [Tes69].One-dimensional [PS93].One-Half [Lir71]. one-step [Spi85].One-Variable [SLZ05]. operand [EM04].Operating [Rot70]. operation [SF93].Operational [BC79]. Operator [von80].Operatorkonzepts [von80].operators [GS82]. optimal [McC77].optimaler [von80]. Optimization [Dan77].Optimizations [BJG+99].Optimized [BM04].Optimizing [LGML05]. order [Abr45].order-differential [KR86].Orders [Alh00b]. Ordinary [Cas83].Oregon [BCDH09]. organization [Sal76].oriented [OY91]. oriyama [SO89].Orlicz [Mus87]. orthogonal [CKL89]. OS/360 [Kuk66]. Other [SR53]. outer [Fuk83].outline [CHGM99].

9

Overconvergence [Ehr89].Overflow [KNS95]. overhead [MI97].Overlapped [PZ95].

p [Fro63]. P.C. [WNO94]. Package [Mat87].packages [Squ91c]. Pade [DF78].pair [HFS99]. paper [Tra60].papers [Spr00, SF59]. parabolic [GST06a].Parallel-array [LC97]. parameter [PS78].parameters [Bus74]. Part [Ben83].partial [Bus74]. Particular [Vol83].parts [Tim87]. Pascal [von80].Pathways [Meg89a]. peaks [Phi79].[Tur69]. 360 [Kuk66]. 370 [ACG+86].6000 [Mar90]. cosine [JL94].overflow [LM07]. performance [CL00].SIAM [IP87]. square [LM99].Pennsylvania [Tra76]. percentage [Fet79].perfect [Dun90]. Performance [Gal85].Performance-Driven [ASA06].periodic [KS88]. perturbed [JS89].phase [CS83]. phenomena [Sti88].pipeline [OJ04]. pipelined [CCCP99].Plane [EW76]. Plethysm [Car90].point [MT72]. Points [FCC73b].pointwise [Som82].pointwise-Lipschitz-continuous [Som82].Polya [EH89]. polycrystals [AM89].Polynomial [SR53]. Polynomials [Bar61].polytype [Vai89]. pomoshch’yu [Saa91].porous [YH89]. Portable [Tan88].Portland [BCDH09]. Positive [Pie84].possible [LM07]. Post [dDEG05].Post-ultimate [dDEG05].posteriori [Kai89]. potential [Sti88].pow [LL09]. power [BF92].Power3TM [AGS99]. powerful [SW88].Powering [PEB04].practitioners [Tho97b]. Precise [Abe88].Precision [Lan64]. Predictive [Bak73].prescaling [LM92]. priblizhenii [DZKK77].priblizheniı [Saa91]. primal [KMY89].primal-dual [KMY89]. primitive [Dri91b].Primitives [Laz85]. Principal [Har97].

priori [Kra87]. priors [GK89a].Probabilities [Whi63].probability [McN73]. problem [EC79].Problems [Ric68]. procedures [Cod82].Proceedings [Boi97]. Process [Whi63].processes [Ebe89]. Processor [Dav81].processors [BBC+91]. product [Gla74].products [LK73]. Professeur [AEF92].Professor [AEF92]. profile [Dav59].program [Wen64]. programmable [LE93].programming [Joh88]. programs [Fuk83].Progress [FLR03]. Project [Loz00].projection [Som82]. projections [Via89].projective [Via89]. proof [Leh83a].proofs [CHGM99]. Properly [HA85].Properties [Kui52]. Proposal [BCK+93].proposed [Hou81]. Provably [Dun87a].proving [Bel89]. Psi [Moo67].Punkte [Bra87].

quad [Mar03]. quadrant [HFS99].Quadratic [POMB05].quadratically [Sch95].quadrature [Akr85]. quality [Atk79].quantities [DP92]. quasi [Cri82].quasi-analytic [Cri82].quaternary [CA00]. question [PKP74].Questions [BL71].

Radial [Pow88]. Radix [Sal51b].radix- [Bak75]. Radix-16 [Erc73].rail [MI97]. Ramanujan [Mim88].random [Sho86]. Range [SOL81].Range-Reduction [BDK+05].Raphson [CHGM99]. rapidly [McC81].rate [DF78]. ratio [Gom89].Rational [Fro61]. Rationale [Dri89].Ratios [Che72]. ratsional’nykh [Saa91].ray [Phi79]. real [Gon52b, GST06a].real-imaginary [BF92]. Realistic [Fra78].Reasoning [CDJ+01].Rechnerarithmetik [von80].reciprocal [FW84]. Reciprocals [SW99a].Reciprocation [ELMT00].

10

recognition [MS82]. record [Sin95].recourse [BW89]. Rectangular [WG94b].Recurrence [GT59]. Recurrences [Tha79].Recursive [Gau99]. reduced [CS83].Reducibility [JMMW79].Reducing [MC93]. reduction [VB81].redundancy [HF95]. redundant [LP83].reelle [Bra87]. reels [Mul85b].region [Fet74]. Regular [Ike75].Related [MR71]. relations [Cri82].remainders [MC93]. remark [MC95].remarks [Hit75].Representation [Kaz65, Mul85b].representations [Bus74].representing [Hai60].requirements [Wil96]. Res [ACG+87].residual [Kaz65]. Residue [OTY91].respect [Bus74]. restoring [LC96].restricted [vdD88]. restrictions [Spi85].result [MC93]. results [VB81].Revised [Dun94b]. revisited [BF92].Richardson [Fil66].Richardson-Algorithmus [Fil66].Riemann [Kol70]. Rigorous [Rum01].RISC [Mar90]. Risch [Laz85].RNC [Ano06]. RNC5 [Ano03].robust [DR04]. ROM [Spr00].Romanian [Hai60]. Romberg [EM86].Root [Wad58]. rooting [WG92].Roots [Sar59]. Rough [Gor82].Rounded [HA85]. rounding [SS93a].Routine [Tur69]. routines [GST02].Royal [Mil75]. Rules [GST03].Runge [Cas83]. Russian [Fog51].

S [Fra81, WOG95]. S-3800 [WOG95].Saddle [FCC73b]. SAIN [Kee82].saturation [Hei88]. Scalable [OJ04].Scalar [ACG+86]. scattering [Kre89].scheme [Kai89]. schemes [CH78].schisleniya [LP83]. Scientific [Mer94].scientists [Lau95]. Searching [SLZ05].second [Gla74]. sections [Rus88].Segment [Lef05]. select [CL00].

Selection [LM95]. selections [Som82].Self [CC69]. Self-contained [CC69].Self-Timed [MIT+95].Semantics [BWKM91]. Seminar [Laz85].Separable [FLMR00]. September [ES89].Sequence [Cod83]. sequences [Gon52b].Service [Loz96a]. set [Meg89a].Sets [PW76]. Seventh [MS94].several [KS88]. Sexagesimal [R. 43].Shared [MIT+95]. sharpened [Kai89].Shifts [BM04]. Short [SF59].Should [PW76]. Shrivenham [MC87].shuffle [SR81]. shuffle-exchange [SR81].SIAM [S+93]. SIGAda [ACM87].Sign [Kah87]. Signals [Sin95].signed [RN96]. signed-digit [CA00].SIGSAM [ACM89]. Similar [Tho66].simple [Wen64]. simplex [Blo88].Simplification [Bro89a].simultaneous [Sun88]. Sine [Tan90c].sine/cosine [JL94]. Single [Fra65].Single- [HHv+73]. single-rail [MI97].singular [Whi82]. singularities [Tim87].singularly [JS89]. sistemakh [LP83].Sivashinsky [AGH89]. Six [WOG95].Sixth [S+93]. size [Bel89]. sloping [Ehr89].small [Shi93]. smooth [KS88].Smoothness [GK89a]. Sobolev [Zie89].Software [Cod71]. solution [DK77].solutions [GST04b]. solving [Fuk83].some [Kui52]. Sound [HJ96].sources [Wil96]. space [Mus87].spaced [FK88]. spaces [Som82].Spanish [MCM90]. special [Bus74].Specific [T+97]. Speculation [CL94b].Speed [SA57]. spherical [PS77].SPIE [Luk99]. splines [DR89].split [WG92]. splitting [Kre89].Square [Wad58]. Square-Root [Wad58].square-rooting [WG92].square-roots [BH99]. Squarers [WS05].squares [Rei86]. squaring [Sar60].SRT [MMH93]. stability [Spi85].stable [Fet74]. stacks [Dem89].

11

Stages [PZ95]. standard [Hou81].Standardfunktionen [Rot70].standardization [Squ91d]. Start [Mar05].Starting [Nin70]. static [MI97].Stations [WNO94]. Statistic [Kra89].statistics [Gom89]. step [Spi85].Stepsize [Spi85]. Stieltjes [BB82].Stirling [Spi71]. Stochastic [Sob88].strange [Wen09]. stratified [Kre89].strictly [Whi82]. Strong [Ebe89].Strongly [Sal92]. structure [EC79].Struve [New84]. Sublinear [BW89].Subprograms [Kuk71].Subroutine [Kod08]. subroutines [Joh88].subsets [Ubh89]. Subsystem [IBM05].subtractive [LO95]. suitable [MT72].Suite [Liu87]. sum [Bus74].summation [Liu95]. Summations [Gla81].Sums [Lir71]. super [Mag94].Supercomputer [WOG95].Supercomputing [Ano91].Supplement [Ske86b]. Supremum [CJL09].sure [Wil96]. surfaces [Lit83].Survey [Fra65]. Switzerland [T+97].symbols [MS82]. Symmetric [SS97b].Symposium [Atk79]. synthesis [BT99].system [Kaz65, ACG+86].System/370 [ACG+87]. System/370 [ACG+86]. System/6000 [Mar90].Systems [Bra87]. systolic [EM86].Szasz [Sun88]. Szasz-Mirakyan [Sun88].Szego [Rus88].

Table [Sal51b]. Table-Driven [Tan89a].Table-Lookup [Tan91b]. Tables [R. 43].tablitsy [Bar72]. Tafeln [Emd45].tail [Fet74]. tail-end [Fet74].taking [BH99]. Tangent [Mar05].TC2 [Boi97]. TC2/WG2.5 [Boi97].teaching [BL71]. Technical [Moo67, SF59].Technique [Vol59]. Techniques [GT59].Teljakowskii [Leh83a]. teooria [Jur66].terms [MV98]. test [Cod82].testing [LMS73]. Tests [Par06]. th [Kog59].

theatres [Sho86]. their [Rit25].theorem [EC79, CK88]. theoretic [VB81].theory [Fog51]. Thiele [Mak80].three [PS79]. threshold [Lit89].throughput [CCC96]. tight [Wil96].Timan [Leh83b]. time [Ebe89].Timed [MIT+95]. Too [Kah04].Topics [Mil75]. Totally [HR88].Trade [Kuk71]. Trade-Off [Kuk71].tradeoff [CL00]. Tradeoffs [WN03].Transcendental [Fil66].transcendentals [LMT98].transfer [GK89a]. transform [Ell83].transformations [Jam81].transforms [Mac72]. Translation [Bai93].Transportable [Cod82].transzendenter [Fil66]. treatment [Hit75].Trig [Sal92]. Trigamma [Spo94].Trigonometric [R. 43]. Truncated [WS05].tsifra [LP83]. tsifroıv [LP83].Tusnady [Ein89]. tutorial [Glo89].Twenty [MS94]. Twenty-Ninth [Sin95].Twenty-Seventh [MS94]. Two [Wad58].type [LW82]. Typed [Sal92].types [EMR82a].

ultimate [dDEG05]. Ultra [EMR82a].Ultra-arithmetic [EMR82a].uncommon [Mac96].Undecidability [Wan74].Undecidable [Ric68]. under/overflow [LM07]. unified [Wal71].Uniform [MR71]. Unifying [Par06].unit [MS82]. Unitary [Leh96].United [Boi97]. units [OJ04].univalent [Rus88]. universal [HSW89].Unrestricted [Bre80]. unstable [AGH89].upper [Fet79]. USA [ES89]. use [Phi79].User [Ful81b]. Using [Kog57].UX [LMOT01].

V. [Kon76]. VA [S+93]. Vail [BC01].Validated [Mer94]. Validation [CK89].Value [Cas83]. Valued [Mat04].

REFERENCES 12

Values [GB68]. Variable [Sal51a].Variable-Stepsize [Ske86a].variables [Sho86]. variation [GK89b].varying [Was89]. Vector [ACG+86].vector-arithmetic [TRHH94].Vegas [AFI69]. Verification [LO95].Verified [DLM09]. versions [LW89].Very [Mit92]. Very-High [LM95].via [GRS87]. Vienna [Mer94].Virtex [WN03]. VLSI [MM92]. Vol [Laz85].voltage [HFS99]. Vychislenie [LCJ63].

W. [Ker83]. Wave [Ike75]. waves [Ehr89].weak [Wil96]. Weakly [Zie89]. well [Vai89].well-behaved [Vai89]. WG2.5 [Boi97].Wide [MMNP91]. wide-range [MV98].Wiener [Deh89]. Windsor [SIJ93].Without [Sar59]. Work [WNO94].Working [Boi97]. workshop [DIW00].Worst [LM03]. Wrigge [Fra81].Writing [DM91].

x [LL09]. X8 [Rot70, Rot70].

Y-MP [KB90]. yield [Mei83].

za [LP83]. zero [Tes69]. zero-finding [Bre75]. zero-overhead [MI97]. Ze-ros [Abr45]. Zeta [Kol70]. Zurich [T+97].

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